Answer
$H$
Work Step by Step
We can use the point-slope form of a line because we are given a point on the graph plus the slope of the graph.
The point-slope equation is as follows:
$y - y_1 = m(x - x_1)$
where $(x_1, y_1)$ is a point on the graph and $m$ is the slope of the graph.
Let us plug in the $x$ and $y$ coordinates of the given point and the given value of the slope into this equation:
$y - (-3) = \dfrac{1}{2}(x - 4)$
Simplify using the distributive property:
$y + 3 = \dfrac{1}{2}x - 4\left(\dfrac{1}{2}\right)$
Multiply to simplify the fraction:
$y + 3 = \dfrac{1}{2}x - 2$
Now, we want to change this equation into slope-intercept form because all the options are in that form.
The slope-intercept form of an equation is given by the following formula:
$y = mx + b$
where $m$ is the slope of the line and $b$ is the y-intercept.
We convert to slope-intercept form by subtracting $3$ from each side of the equation:
$y = \dfrac{1}{2}x - 2 - 3$
$y = \frac{1}{2}x - 5$
This corresponds to option $H$.
